Translator Disclaimer
December 2017 Targeted sequential design for targeted learning inference of the optimal treatment rule and its mean reward
Antoine Chambaz, Wenjing Zheng, Mark J. van der Laan
Ann. Statist. 45(6): 2537-2564 (December 2017). DOI: 10.1214/16-AOS1534

Abstract

This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the nonexceptional case, that is, assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption.

Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Our main result is a central limit theorem which enables the construction of confidence intervals on both mean rewards under the current estimate of the optimal TR and under the optimal TR itself. The asymptotic variance of the estimator takes the form of the variance of an efficient influence curve at a limiting distribution, allowing to discuss the efficiency of inference.

As a by product, we also derive confidence intervals on two cumulated pseudo-regrets, a key notion in the study of bandits problems.

A simulation study illustrates the procedure. One of the cornerstones of the theoretical study is a new maximal inequality for martingales with respect to the uniform entropy integral.

Citation

Download Citation

Antoine Chambaz. Wenjing Zheng. Mark J. van der Laan. "Targeted sequential design for targeted learning inference of the optimal treatment rule and its mean reward." Ann. Statist. 45 (6) 2537 - 2564, December 2017. https://doi.org/10.1214/16-AOS1534

Information

Received: 1 April 2016; Revised: 1 September 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838142
MathSciNet: MR3737901
Digital Object Identifier: 10.1214/16-AOS1534

Subjects:
Primary: 62G05, 62G20
Secondary: 62K99

Rights: Copyright © 2017 Institute of Mathematical Statistics

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.45 • No. 6 • December 2017
Back to Top